Method for determining signal quality in optical transmission systems

ABSTRACT

A method for determining signal quality in optical transmission systems, wherein the effective signal-to-noise ratio is determined by measuring amplitude histograms of a signal and by calculating characteristic histogram moments and additional interference is ascertained by comparing the characteristic histogram moments with the optical signal-to-noise ratio.

BACKGROUND OF THE INVENTION

[0001] The present invention relates to a method for determining thesignal quality in optical transmission systems and for determininginterfering effects.

[0002] In the future, transmission networks will be embodied as opticalnetworks via which data will be transmitted at extremely high bit ratesusing the wavelength division multiplex method. In this context,extensive transparency of the networks is sought. However, in therequired monitoring of the signal quality, it is then no longer possibleto ascertain a violation of code rules; for example, in the case oferror correcting codes. Therefore, methods are being developed whichenable the signal quality to be assessed independently thereof.

[0003] In a method described in published patent application DE 195 04856, amplitude samples are taken asynchronously with respect to thesignal clock and the central moments of the sample are calculatedtherefrom. These are then compared with empirically obtained referencevalues in order to derive therefrom a statement about the signalquality.

[0004] Patent application DE 198 12 078 specifies a further method fordetermining the signal quality, which makes it possible to make reliablestatements about the signal quality. In this method, the outer edges ofa histogram which specifies the probability of the occurrence ofdifferent voltage values representing the logic states 0 and 1 areevaluated.

[0005] This method is developed further in an earlier application DE 19914 793. In this case, the measuring arrangements allow not only a shiftof the thresholds but also a shift of the sampling instants, as a resultof which the eye opening can be determined. The determination of thedistribution densities of the samples as a function of the amplitudevalues is effected by deriving a probability distribution whichspecifies the frequency of the occurrence of one of the two binarystates as a function of the sampling threshold.

[0006] Attempts likewise are being made to obtain from the histogramsknowledge about interfering influences on the transmission link.However, if different interfering effects occur simultaneously, theevaluation of the probability density distribution suffices foridentifying and quantifying the effects. In the event of thesimultaneous transmission of a number of signals, multichannel effectsthat occur, such as cross phase modulation (XPM), four wave mixing(FWM), stimulated Raman cross-talk (SRS-XT) and coherent/incoherentcross-talk (XT), all bring about, on statistical average, a Gaussianwidening of the probability density distribution of sampling amplitudesand are, thus, indistinguishable.

[0007] It is an object of the present invention to specify a method withwhich the signal quality can be determined as well as the essentialtransmission properties. Furthermore, the present intention is toidentify interfering effects and ascertain the magnitude thereof.

SUMMARY OF THE INVENTION

[0008] Accordingly, in an embodiment of the present invention, a methodis provided for determining signal quality in optical transmissionsystems by measuring an amplitude histogram of a signal, wherein themethod includes the steps of: calculating characteristic histogrammoments for determining an effective signal-to-noise ratio; andassigning the characteristic histogram moments, for further determiningthe effective signal-to-noise ratio, to an optical signal-to-noise ratioof a transmission system that is not impaired by further interferenceeffects.

[0009] In a further embodiment of the present invention, a method isprovided for determining signal quality and optical transmission systemsby measuring an amplitude histogram of a signal, wherein the methodincludes the steps of: calculating characteristic histogram moments todetermine the signal quality; measuring an optical signal-to-noise ratiodirectly; comparing the characteristic histogram moments with themeasured optical signal-to-noise ratio; and determining, if thecomparison yields non-correspondence, a proportion of nonlinear noise.

[0010] A key advantage of the method according to the present inventionis that histogram measurements can be used to infer the effectivesignal-to-noise ratio of a signal. An additional signal-to-noise ratiomeasurement can be used to make a reliable statement about the presenceof additional interference effects, which then can be examined moreprecisely.

[0011] On the basis of calculations or comparative measurements with asystem disturbed only by noise, it is possible to make statements aboutthe magnitude of the additional interference influences.

[0012] Mathematical transformations, in particular, enable a simplecomparison between measured histogram values and calculated or measuredcomparison values, since a histogram moments term containing averagevalues and variances of the sampling amplitude distributions of thebinary states is linearly dependent on the signal-to-noise ratio.

[0013] Additional features and advantages of the present invention aredescribed in, and will be apparent from, the following DetailedDescription of the Invention and the Figures.

BRIEF DESCRIPTION OF THE FIGURES

[0014]FIG. 1 shows a known measuring arrangement for generatingamplitude histograms.

[0015]FIG. 2 shows an amplitude histogram.

[0016]FIG. 3 shows a basic circuit diagram of an optical receiver.

[0017]FIG. 4 shows amplitude histograms for different signal-to-noiseratios.

[0018]FIG. 5 shows a measuring arrangement.

[0019]FIG. 6 shows a histogram signal-to-noise ratio diagram.

DETAILED DESCRIPTION OF THE INVENTION

[0020] The known measuring device 1 for amplitude histograms which isillustrated in FIG. 1 serves for determining the probability densitydistribution of samples through measurements at different samplingthresholds.

[0021] The measuring device 1 contains two decision stages 2 and 3, towhose first inputs an already converted electrical signal S_(E) is fedvia a data signal input IN, the signal having been transmittedbeforehand as an optical signal via a link section or the entiretransmission link. The decision threshold of at least one of thedecision stages 2 and 3 is adjustable via a controller 11; here throughthe application of comparison voltages corresponding to threshold valuesS1 and S2.

[0022] The outputs of the decision stages are respectively connected toa sampling flip-flop 4 and 5, whose data outputs are fed to anExclusive-OR gate 7. The output of this gate is connected to an errorcounter 8 which, like a computing circuit 9, is part of a histogramcomputer 10.

[0023] Moreover, a clock regenerator 6 is provided, which regeneratesthe bit clock signal TS from the received data signal via a phase-lockedloop.

[0024] The electrical signal S_(E) is compared in parallel withdifferent threshold values S1 and S2, sampled and stored as binaryvalues. Different measurements can be carried out by the measuringdevice. One threshold value S1 may be kept constant as desired thresholdvalue and the other threshold value S2 may be varied. The “errors” FE(different sampling states 0 and 1 in the sampling flip-flops; FIG. 1)which occur at different threshold values S2 are evaluated, a uniformdistribution of logic zeros and ones being assumed or the distributionbeing measured. The errors related to the bits received overall yieldthe error rate distribution VF as a function of the threshold value S2,which distribution is represented by a broken line in FIG. 2. This canbe converted into a probability density distribution VD; that is to say,into a sampling amplitude distribution for “0's” and “1's”. The bars inthe amplitude histogram in FIG. 2 specify the (relative) number ofsamples for the logic states “0” and “1” which occur between equidistantvalues. The average values are designated by μ₀ and μ₁ and the standarddeviations (moments) are designated by σ₀ and σ₁. Amplitude histogramscan be plotted as a function of the threshold value S2 or of thesampling amplitude A (voltage values or corresponding current values ofan opto-electrical transducer). The relative frequencies P are, in eachcase, plotted on the ordinate. The sampling instant is kept constant.However, it is also possible to create histograms that are dependent onthe threshold value and the phase angle of the sampling clock, but thesewill not be discussed in further detail in the exemplary embodiment.

[0025] It is also equally possible to determine expected values VS0 forthe occurrence of logic zeros (or logic ones) in dependence on thevariable threshold S2, which is represented by a dash-dotted line asnormalized function VS0 in FIG. 2, and can be converted into theamplitude distribution VD by differentiation.

[0026] The sampled data signal is output at the data output DO, thecharacteristic histogram data in each case at the end of a sufficientlylong measurement period at the output HO of the histogram computer.

[0027] It is likewise possible to measure the distribution of thesampling amplitudes directly. This requires a storage oscilloscope withan optical input or an opto-electrical transducer connected upstreamwhich, at an adjustable sampling instant, records the received signalwith regard to its amplitude (eye pattern) and statistically evaluatesit.

[0028] For the further considerations it is possible to use each of theamplitude histograms, the error rate distribution FE, a probabilitydistribution VS0 for a logic state and probability density distributionVD since these can be converted into one another.

[0029] In order to assess the signal or transmission quality, theamplitude histogram is recorded and the characteristic histogrammoments, average values and variance are determined.

[0030] The effective signal-to-noise ratio can be determined therefrom,as will be explained. A further direct measurement of thesignal-to-noise ratio via an optical spectrum analyzer and a comparisonof this directly measured signal-to-noise ratio with the effectivesignal-to-noise ratio determined from the characteristic histogrammoments may follow. If values which correspond to one another for anoptimum system are present, the system has, except for the noise, nofurther interference influences.

[0031] However, if the effective signal-to-noise ratio determined fromthe amplitude histogram corresponds to a signal-to-noise ratio that isless than the directly measured signal-to-noise ratio, then additionalimpairments due to nonlinear effects are present.

[0032] The relationship between the characteristic moments μ and σ ofthe histogram and the signal-to-noise ratio can be determined viameasurements on an ideal system. It can be calculated equally on thebasis of the explanations below. These will also clarify therelationships between the characteristic values of the histogram and thesignal-to-noise ratio.

[0033]FIG. 3 illustrates an input stage of an optical receiver as abasic circuit diagram. This contains an optical preamplifier 12, anoptical filter 13, an opto-electrical transducer 14 and an electricalfilter 15, which determines the electrical bandwidth.

[0034] The optical signal S₀ is fed to the optical preamplifier 12,amplified there and subsequently limited in its bandwidth by the filter13. After conversion into an electrical voltage signal S_(E), the latteris band-limited by an electrical filter 15 (the band limiting can beeffected by circuit elements).

[0035] The photodiode currents corresponding to samples are used in theconsiderations below. The (e.g., received) signal S_(E) to be measuredincludes the data signal and a noise component.

[0036] The photocurrent, corresponding to the signal, I_(E)=I_(S)+ΔI ofa photodetector or opto-electrical transducer is the sum of the (useful)data signal component I_(S)=

P_(v)(AA) and the noise component ΔI.

[0037] For its part, the data signal component I_(S) is dependent on thedetector sensitivity

=ηq/hv (where η=quantum efficiency, q=elementary charge, h=quantum ofaction, v=frequency of the signal) and the amplified signal powerP_(v)=GP_(S)+P_(sp). The signal power P is, in turn, composed of thesignal power P_(S) and the proportion caused by spontaneous emissionP_(sp). In this case, G corresponds to the gain factor of the opticalamplifier 12. The power of the spontaneous emission, withP_(sp)=2S_(sp)B_(opt), results from the spectral density S_(sp) thereofand the optical bandwidth B_(opt) limited on account of an opticalfilter 4 upstream of the photodiode. (G. P. Agrawal, Fiber OpticCommunication Systems, 2nd Edition, pp. 404 to 406)

[0038] The noise component ΔI is composed of the proportions of thermalnoise, shot noise and noise due to spontaneous emission processes. Theindividual noise power contributions (noise current contributions) orvariance contributions such as the thermal noise σ_(t  h)²,

[0039] the shot noise σ_(s  h)²

[0040] and the so-called beat noise of the spontaneous emission throughmixing with itself σ_(s  p − s  p)²

[0041] and with the useful signal S  σ_(S − s  p)²

[0042] add up, assuming a Gaussian distribution, to form a totalvariance σ²=<ΔI²>. (G. P. Agrawal, Fiber Optic Communication Systems,2nd Edition, pp. 404 to 405; J. H. Winters, R. D. Gitlin, IEEE Trans. OnCommunication, 38, pp. 1439 to 1453) $\begin{matrix}{\sigma^{2} = {\sigma_{t\quad h}^{2} + \sigma_{s\quad h}^{2} + \sigma_{{s\quad p} - {s\quad p}}^{2} + \sigma_{S - {s\quad p}}^{2}}} & (1)\end{matrix}$

[0043] the constituents can be described by [3]: $\begin{matrix}{\sigma_{t\quad h}^{2} = {4k_{B}T\quad F\quad {B_{e\quad l}/R_{l}}}} & (2) \\{\sigma_{s\quad h}^{2} = {2{q\left\lbrack {{\left( {{G\quad P_{S}} + P_{s\quad p}} \right)} + I_{d}} \right\rbrack}B_{e\quad l}}} & (3) \\{\sigma_{{s\quad p} - {s\quad p}}^{2} = {4^{2}S_{s\quad p}^{2}B_{o\quad p\quad t}B_{e\quad l}}} & (4) \\{\sigma_{S - {s\quad p}}^{2} = {4^{2}G\quad P_{S}S_{s\quad p}B_{e\quad l}}} & (5)\end{matrix}$

[0044] In this case, in detail: k_(B) is Boltzmann's constant, T is theabsolute temperature, F is the noise figure of the optical amplifier,B_(el) describes the electrical bandwidth of the photodiode, R₁ takesaccount of the charging resistance, q is the elementary charge, I_(d) isthe dark current of the detector, S_(sp) is the spectral density of thespontaneous emission and B_(opt) corresponds to the optical bandwidth(usually determined by the optical demultiplexer).

[0045] The optical signal-to-noise ratio (OSNR) at the input of thephotodiode is determined by the noise behavior of the opticalpreamplifier. The OSNR at the output of an optical amplifier OV can becalculated by [G. P. Agrawal, Fiber Optic Communication Systems, 2ndEdition, pp. 365, 366; Yariv, Opt. Letters 1, (1990), pages 1064-1064]:$\begin{matrix}{{O\quad S\quad N\quad R} = \frac{{\langle P\rangle}_{a\quad v}}{2S_{s\quad p}B_{o\quad p\quad t}^{O\quad S\quad N\quad R}}} & (6)\end{matrix}$

[0046] with the average signal power <P>_(av) and the optical bandwidthB_(o  p  t)^(O  S  N  R),

[0047] to which the OSNR value relates. Consequently, the value to bemeasured, the OSNR present at the input of the photodiode, can beintroduced into equations (3)-(5): $\begin{matrix}{\sigma_{s\quad h}^{2} = {2{q\left\lbrack {{\left( {{G\quad P_{S}} + \frac{{\langle P\rangle}_{a\quad v}B_{o\quad p\quad t}}{O\quad S\quad N\quad {R \cdot B_{o\quad p\quad t}^{O\quad S\quad N\quad R}}}} \right)} + I_{d}} \right\rbrack}B_{e\quad l}}} & (7) \\{\sigma_{{s\quad p} - {s\quad p}}^{2} = {{^{2}\left( \frac{{\langle P\rangle}_{a\quad v}}{O\quad S\quad N\quad {R \cdot B_{o\quad p\quad t}^{O\quad S\quad N\quad R}}} \right)}^{2}B_{o\quad p\quad t}B_{e\quad l}}} & (8) \\{\sigma_{S - {s\quad p}}^{2} = {2^{2}G\quad P_{S}\frac{{\langle P\rangle}_{a\quad v}}{O\quad S\quad N\quad {R \cdot B_{o\quad p\quad t}^{O\quad S\quad N\quad R}}}B_{e\quad l}}} & (9)\end{matrix}$

[0048] The average values μ₀, μ₁ and standard deviations σ₀, σ₁ andvariances σ₀ ², σ₁ ² (square of the standard deviations) of the Gaussiandistributions are, in each case, determined for both binary states, “0”and “1”.

[0049] The unadulterated signal current component I_(S) _(—) _(0,1)=

GP_(S) _(—) _(0,1) in equations (7) and (9) thus can be replaced by therespective average values μ₀, μ₁. As a result of the formation of thedifference in the total variance (1) of the distributions of the “0's”and “1's”, the contributions (2) and (4), which are independent ofsignal levels corresponding to the logic states of the data signal,cancel one another out and the following is obtained from (7) and (9):$\begin{matrix}{{{{\sigma_{1}^{2} - \sigma_{0}^{2}} = {{{2q\quad \mu_{1}B_{e\quad l}} + {2{\mu}_{1}\frac{{\langle P\rangle}_{a\quad v}B_{e\quad l}}{O\quad S\quad N\quad {R \cdot B_{o\quad p\quad t}^{O\quad S\quad N\quad R}}}} - {2q\quad \mu_{0}B_{e\quad l}} - {2{\mu}_{0}\frac{{\langle P\rangle}_{a\quad v}B_{e\quad l}}{O\quad S\quad N\quad {R \cdot B_{o\quad p\quad t}^{O\quad S\quad N\quad R}}}}} = {\left( {{2q\quad B_{e\quad l}} + {2\frac{{\langle P\rangle}_{a\quad v}B_{e\quad l}}{O\quad S\quad N\quad {R \cdot B_{o\quad p\quad t}^{O\quad S\quad N\quad R}}}}} \right)\left( {\mu_{1} - \mu_{0}} \right)}}}\quad {a\quad n\quad d\quad h\quad e\quad n\quad c\quad e}}{\quad \quad}} & (10) \\{\frac{\sigma_{1}^{2} - \sigma_{0}^{2}}{\mu_{1} - \mu_{2}} = {2\left( {q + \frac{{\langle P\rangle}_{a\quad v}}{O\quad S\quad N\quad {R \cdot B_{o\quad p\quad t}^{O\quad S\quad N\quad R}}}} \right)B_{e\quad l}}} & (11)\end{matrix}$

[0050] The free parameters on the right-hand side of (11) must be known,but also can be determined by a reference measurement given a knownsignal-to-noise ratio. In optically preamplified systems thecontribution of the shot noise can be disregarded, so that the term2qB_(el) on the right-hand side of (11) can be omitted. A simplifiedrelationship between OSNR and measured average values and variances isthus produced: $\begin{matrix}{{101{g\left( \frac{\mu_{1} - \mu_{0}}{\sigma_{1}^{2} - \sigma_{0}^{2}} \right)}} = {{101{g\left( {O\quad S\quad N\quad R} \right)}} - {101{g\left( \frac{2{\langle P\rangle}_{a\quad v}B_{e\quad l}}{B_{o\quad p\quad t}^{O\quad S\quad {NR}}} \right)}}}} & (12)\end{matrix}$

[0051] This corresponds to a linear equation in a logarithmicrepresentation. In the case of a system disturbed only by optical noise,the signal-to-noise ratio therefore can be determined by calculating thecharacteristic values of the histogram. The first term of equation 12 isreferred to below as histogram moments term HMT.

[0052] Histograms for various signal-to-noise ratios are indicated inFIG. 4. Smaller signal-to-noise ratios lead to maxima that are spreadfurther apart but are flatter.

[0053] From the average values μ₀ and μ₁ of the Gaussian distributionsfor logic O's and 1's and their variances σ₀ ², σ₁ ² for varioussignal-to-noise ratios, it is possible to determine the resultantstraight line for the distributions by minimizing the squares of thedeviations. The function described by equation (12) is illustrated inthe signal-to-noise ratio histogram moments diagram of FIG. 5.

[0054] The calculated reference straight line, or one determined bymeasurements, can be used for evaluating present histograms.

[0055] In the case of a system which is free of nonlinear effects (andother effects which do not influence the amplitude histograms, apartfrom noise), the signal-to-noise ratio can, therefore, be determinedusing the reference straight line by measuring the characteristic valuesof the histogram. Measurements for different signal levels orsignal-to-noise ratios, apart from measurement errors or inaccuracies,all lie on the reference straight line.

[0056] It generally is not known whether nonlinear effects occur whichinfluence the histogram and reduce the “effective” signal-to-noiseratio. Therefore, the method is designated more exactly as determinationof the effective signal-to-noise ratio OSNR_(eff). In the absence of theinterfering (nonlinear) effects including cross-talk between a number ofchannels, the measurement yields the signal-to-noise ratio directly. Asmentioned above, due to the statistical properties of some nonlineareffects, the latter act like an additional noise contribution σ² _(n1)which produces an increased effective variance σ² _(eff) in theamplitude histogram: $\begin{matrix}{\sigma_{eff}^{2} = {\sigma_{t\quad h}^{2} + \sigma_{s\quad h}^{2} + \sigma_{{s\quad p} - {s\quad p}}^{2} + \sigma_{S - {s\quad p}}^{2} + \sigma_{n\quad l}^{2}}} & (13)\end{matrix}$

[0057] The total “effective signal-to-noise ratio” OSNR_(eff)consequently can be determined via average values μ₀ and μ₁ and thevariances σ₀ ² and σ₁ ² of the amplitude distributions of the “0's” and“1's”, and the noise component of the nonlinear effects (likewisecross-talk in the case of multichannel systems) can be determined bycomparison with the calculated values of a system having no nonlinear orinterfering effects.

[0058] Instead of a calculation, the optical signal-to-noise ratioOSNR_(di) can be measured directly.

[0059]FIG. 6 illustrates a corresponding arrangement. The lattercontains the already described measuring device 1, a furthersignal-to-noise ratio measuring device 18 and a comparison device 19 forthe evaluation of the measured values.

[0060] The binary optical signal S₀ is first fed via a switch 16 and anopto-electrical transducer 17 to the measuring device 1, which recordsthe amplitude histogram and determines the histogram moments. Theoptical signal-to-noise ratio OSNR is then measured directly by thesignal-to-noise ratio measuring device 18 (optical spectrum analyzer),in which case all known measurement methods can be employed and, ifappropriate, at least the transmission of some signals is interrupted.The measurement results are evaluated in the comparison device 19.

[0061] If the value on the reference straight line which is determinedfrom the histogram corresponds to the directly measured opticalsignal-to-noise ratio, no interfering effects are present. By contrast,if the value on the reference straight line which is determined from thehistogram moments in FIG. 5 on the left lies below the directly measuredsignal-to-noise ratio OSNR_(di), then the difference OSNR_(n1) is causedby additional interference effects and it is possible to search for thecauses, such as cross phase modulation (XPM), four wave mixing (FWM),stimulated Raman cross-talk (SRS-XT) and coherent/incoherent cross-talk(XT), and also further causes such as self phase modulation (SPM) andpolarization mode dispersion (PMD).

[0062] As already mentioned, the determination of the signal-to-noiseratio need not be effected using a representation according to FIG. 5,but rather can be carried out using non-logarithmic diagrams, tables, orusing the calculated values etc.

[0063] It should also be added that the histograms and thus thedeterminations of the signal-to-noise ratio are largely independent ofthe dispersion.

[0064] Indeed, although the present invention has been described withreference to specific embodiments, those of skill in the art willrecognize that changes may be made thereto without departing from thespirit and scope of the invention as set forth in the hereafter appendedclaims.

1. A method for determining signal quality in optical transmissionsystems by measuring an amplitude histogram of a signal, the methodcomprising the steps of: calculating characteristic histogram momentsfor determining an effective signal-to-noise ratio, the characteristichistogram moments including average values of amplitude distributionsand standard deviations of the amplitude distributions; and assigningthe characteristic histogram moments, for further determining theeffective signal-to-noise ratio, to an optical signal-to-noise ratio ofa transmission system that is not impaired by further interferenceeffects.
 2. A method for determining signal quality in opticaltransmission systems by measuring an amplitude histogram of a signal,the method comprising the steps of: calculating characteristic histogrammoments to determine the signal quality; measuring directly an opticalsignal-to noise ratio; comparing the characteristic histogram momentswith the measured optical signal-to-noise ratio; and determining, if thecomparison yields non-correspondence, a proportion of non-linear noise.3. A method for determining signal quality in optical transmissionsystems by measuring an amplitude histogram of a signal as claimed inclaim 1, the method further comprising the steps of: determiningdifferences between the average values of the amplitude distributionsregarded as Gaussian distribution for logic “1's” and logic “0's”;determining differences between variances of the amplitude distributionsfor logic “1's” and logic “0's”; and determining a histogram momentsterm by forming a quotient from the two differences.
 4. A method fordetermining signal quality in optical transmission systems by measuringan amplitude histogram of a signal as claimed in claim 2, the methodfurther comprising the steps of: determining differences between theaverage values of the amplitude distributions regarded as Gaussiandistribution for logic “1's” and logic “0's”; determining differencesbetween variances of the amplitude distributions for logic “1's” andlogic “0's”; and determining a histogram moments term by forming aquotient from the two differences.
 5. A method for determining signalquality in optical transmission systems by measuring an amplitudehistogram of a signal as claimed in claim 1, wherein, as the amplitudehistogram, measurement is made of one of an error rate distribution independence on a variable sampling threshold, a distribution density oflogic “0's” or logic “1's” in dependence on the variable samplingthreshold, and a probability density distribution of sampling amplitudesof logic “0's and logic “1's,” and wherein the characteristic histogramvalues are respectively determined in each case.
 6. A method fordetermining signal quality in optical transmission systems by measuringan amplitude histogram of a signal as claimed in claim 2, wherein, asthe amplitude histogram, measurement is made of one of an error ratedistribution in dependence on a variable sampling threshold, adistribution density of logic “0's” or logic “1's” in dependence on thevariable sampling threshold, and a probability density distribution ofsampling amplitudes of logic “0's and logic “1's,” and wherein thecharacteristic histogram values are respectively determined in eachcase.
 7. A method for determining signal quality in optical transmissionsystems by measuring an amplitude histogram of a signal as claimed inclaim 1, wherein the corresponding characteristic histogram moments arecalculated in dependence on a signal-to-noise ratio of a transmissionsystem having no link influences.
 8. A method for determining signalquality in optical transmission systems by measuring an amplitudehistogram of a signal as claimed in claim 2, wherein the correspondingcharacteristic histogram moments are calculated in dependence on asignal-to-noise ratio of a transmission system having no linkinfluences.
 9. A method for determining signal quality in opticaltransmission systems by measuring an amplitude histogram of a signal asclaimed in claim 1, wherein the characteristic histogram moments arecalculated in dependence on a signal-to-noise ratio without linkinfluences for an optimum system.
 10. A method for determining signalquality in optical transmission systems by measuring an amplitudehistogram of a signal as claimed in claim 2, wherein the characteristichistogram moments are calculated in dependence on a signal-to-noiseratio without link influences for an optimum system.
 11. A method fordetermining signal quality in optical transmission systems by measuringan amplitude histogram of a signal as claimed in claim 5, wherein thecharacteristic histogram moments and associated signal-to-noise ratiosare stored.
 12. A method for determining signal quality in opticaltransmission systems by measuring an amplitude histogram of a signal asclaimed in claim 6, wherein the characteristic histogram moments andassociated signal-to-noise ratios are stored.
 13. A method fordetermining signal quality in optical transmission systems by measuringan amplitude histogram of a signal as claimed in claim 7, wherein thecharacteristic histogram moments and associated signal-to-noise ratiosare stored.
 14. A method for determining signal quality in opticaltransmission systems by measuring an amplitude histogram of a signal asclaimed in claim 8, wherein the characteristic histogram moments andassociated signal-to-noise ratios are stored.
 15. A method fordetermining signal quality in optical transmission systems by measuringan amplitude histogram of a signal as claimed in claim 3, wherein afunction of the characteristic histogram moments is stored in dependenceon the signal-to-noise ratio.
 16. A method for determining signalquality in optical transmission systems by measuring an amplitudehistogram of a signal as claimed in claim 4, wherein a function of thecharacteristic histogram moments is stored in dependence on thesignal-to-noise ratio.
 17. A method for determining signal quality inoptical transmission systems by measuring an amplitude histogram of asignal as claimed in claim 5, wherein a function of the characteristichistogram moments is stored in dependence on the signal-to-noise ratio.18. A method for determining signal quality in optical transmissionsystems by measuring an amplitude histogram of a signal as claimed inclaim 6, wherein a function of the characteristic histogram moments isstored in dependence on the signal-to-noise ratio.
 19. A method fordetermining signal quality in optical transmission systems by measuringan amplitude histogram of a signal as claimed in claim 1, wherein arelationship between the characteristic histogram moments andsignal-to-noise ratio is determined using the following equation,including mathematical transformations: or${101{g\left( \frac{\mu_{1} - \mu_{0}}{\sigma_{1}^{2} - \sigma_{0}^{2}} \right)}} = {{101{g\left( {O\quad S\quad N\quad R} \right)}} - {101{g\left( \frac{2{\langle P\rangle}_{a\quad v}B_{e\quad l}}{B_{o\quad p\quad t}^{O\quad S\quad {NR}}} \right)}}}$${o\quad {r\left( \frac{\mu_{1} - \mu_{0}}{\sigma_{1}^{2} - \sigma_{0}^{2}} \right)}} = {\left( {O\quad S\quad N\quad R} \right)/{\left( \frac{2{\langle P\rangle}_{a\quad v}B_{e\quad l}}{B_{o\quad p\quad t}^{O\quad S\quad {NR}}} \right).}}$

where μ₀ to and μ₁ are average values of the amplitude distribution ofthe logic “1's” and “0's”, σ₀ and σ₁ are standard deviations of theamplitude distribution of the logic “1's” and “0's”, OSNR issignal-to-noise ratio <P>_(av) is an average signal power,B_(o  p  t)^(O  S  N  R)

is an optical bandwidth, B_(el) is an electrical bandwidth of aphotodiode or an opto-electrical transducer, and

=ηq/hv is detector sensitivity (η=quantum efficiency, q=elementarycharge, h=quantum of action, v=frequency of the signal).
 20. A methodfor determining signal quality in optical transmission systems bymeasuring an amplitude histogram of a signal as claimed in claim 2,wherein a relationship between the characteristic histogram moments andsignal-to-noise ratio is determined using the following equation,including mathematical transformations: or${101{g\left( \frac{\mu_{1} - \mu_{0}}{\sigma_{1}^{2} - \sigma_{0}^{2}} \right)}} = {{101{g\left( {O\quad S\quad N\quad R} \right)}} - {101{g\left( \frac{2{\langle P\rangle}_{a\quad v}B_{e\quad l}}{B_{o\quad p\quad t}^{O\quad S\quad {NR}}} \right)}}}$${o\quad {r\left( \frac{\mu_{1} - \mu_{0}}{\sigma_{1}^{2} - \sigma_{0}^{2}} \right)}} = {\left( {O\quad S\quad N\quad R} \right)/{\left( \frac{2{\langle P\rangle}_{a\quad v}B_{e\quad l}}{B_{o\quad p\quad t}^{O\quad S\quad {NR}}} \right).}}$

where μ₀ and μ₁ are average values of the amplitude distribution of thelogic “1's” and “0's”, σ₀ and σ₁ are standard deviations of theamplitude distribution of the logic “1's” and “0's”, OSNR issignal-to-noise ratio <P>_(av) is an average signal power,B_(o  p  t)^(O  S  N  R)

is an optical bandwidth, B_(el) is an electrical bandwidth of aphotodiode or an opto-electrical transducer, and

=ηq/hv is detector sensitivity (η=quantum efficiency, q=elementarycharge, h=quantum of action, v=frequency of the signal).
 21. A methodfor determining signal quality in optical transmission systems bymeasuring an amplitude histogram of a signal as claimed in claim 19,wherein the term$\left( \frac{2{\langle P\rangle}_{a\quad v}B_{e\quad l}}{B_{o\quad p\quad t}^{O\quad S\quad {NR}}} \right)$

of the equation is determined by measurement.
 22. A method fordetermining signal quality in optical transmission systems by measuringan amplitude histogram of a signal as claimed in claim 20, wherein theterm$\left( \frac{2{\langle P\rangle}_{a\quad v}B_{e\quad l}}{B_{o\quad p\quad t}^{O\quad S\quad {NR}}} \right)$

of the equation is determined by measurement.